Gradient norm minimizations

Gradient Norm Minimizations 14.5.9 Netvton-Raphson Methods 14.5.10 Gradient Extremal Methods Constrained Optimization Problems Locating the Global Minimum and Conformational Sampling 333 333 338 338 339 Appendix C First and Second Quantization Reference 411 411 412... 

Gradient Extremal (GE), 338 Gradient norm minimization, 333 Gradient of a function, 238 Greens function, 257 GROMOS force field, 40 Gross atomic charge, 218... 

Figure 12.10 shows an example of a one-dimensional function and its associated gradient norm. It is clear that a gradient norm minimization will only locate one of the two stationary points if started near x = 1 or x = 9. Most other starting points will converge on the shallow part of the function near x = 5. The often very small convergence radius makes gradient norm minimizations impractical for routine use. 

The calculated energy of stabilization of such an adduct (DZ-type basis set) is about 5 kcal/mol. Structure IV corresponds to the transition state of bimolecular addition of HCl to ethylene localized by the gradient norm minimization method. 

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